Three-dimensional theory of weakly nonlinear Compton scattering

Abstract

Nonlinear effects are known to occur in light sources when the wiggler parameter, or normalized 4-potential, A=e−AμAμ/m0c, approaches unity. In this paper, it is shown that nonlinear spectral features can appear at arbitrarily low values of A if the fractional bandwidth of the undulator, Δϕ−1, is sufficiently small and satisfies the condition A2Δϕ∼1. Consequences for the spectral brightness of Compton scattering light sources are outlined. Compton and Thomson scattering theories are compared with the Klein–Nishina cross-section formula to highlight differences in the case of narrow band gamma-ray operation. A weakly nonlinear Compton scattering theory is developed in one (plane wave) and three (local plane wave approximation) dimensions. Analytical models are presented and benchmarked against numerical calculations solving the Lorentz force equation with a fourth-order Runge–Kutta algorithm. Finally, narrow band gamma-ray spectra are calculated for realistic laser and electron beams.